{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T14:14:11Z","timestamp":1779372851256,"version":"3.53.1"},"reference-count":51,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T00:00:00Z","timestamp":1683763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Rijeka","award":["uniri-mladi-tehnic-22-16"],"award-info":[{"award-number":["uniri-mladi-tehnic-22-16"]}]},{"name":"University of Rijeka","award":["uniri-tehnic-18-17"],"award-info":[{"award-number":["uniri-tehnic-18-17"]}]},{"name":"Computer-Aided Digital Analysis And Classification of Signals","award":["uniri-mladi-tehnic-22-16"],"award-info":[{"award-number":["uniri-mladi-tehnic-22-16"]}]},{"name":"Computer-Aided Digital Analysis And Classification of Signals","award":["uniri-tehnic-18-17"],"award-info":[{"award-number":["uniri-tehnic-18-17"]}]},{"name":"ZIP UNIRI project","award":["uniri-mladi-tehnic-22-16"],"award-info":[{"award-number":["uniri-mladi-tehnic-22-16"]}]},{"name":"ZIP UNIRI project","award":["uniri-tehnic-18-17"],"award-info":[{"award-number":["uniri-tehnic-18-17"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Instantaneous frequency (IF) is commonly used in the analysis of electroencephalogram (EEG) signals to detect oscillatory-type seizures. However, IF cannot be used to analyze seizures that appear as spikes. In this paper, we present a novel method for the automatic estimation of IF and group delay (GD) in order to detect seizures with both spike and oscillatory characteristics. Unlike previous methods that use IF alone, the proposed method utilizes information obtained from localized R\u00e9nyi entropies (LREs) to generate a binary map that automatically identifies regions requiring a different estimation strategy. The method combines IF estimation algorithms for multicomponent signals with time and frequency support information to improve signal ridge estimation in the time\u2013frequency distribution (TFD). Our experimental results indicate the superiority of the proposed combined IF and GD estimation approach over the IF estimation alone, without requiring any prior knowledge about the input signal. The LRE-based mean squared error and mean absolute error metrics showed improvements of up to 95.70% and 86.79%, respectively, for synthetic signals and up to 46.45% and 36.61% for real-life EEG seizure signals.<\/jats:p>","DOI":"10.3390\/s23104680","type":"journal-article","created":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T01:30:29Z","timestamp":1683855029000},"page":"4680","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Method for Automatic Estimation of Instantaneous Frequency and Group Delay in Time\u2013Frequency Distributions with Application in EEG Seizure Signals Analysis"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1466-1534","authenticated-orcid":false,"given":"Vedran","family":"Jurdana","sequence":"first","affiliation":[{"name":"Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1036-9261","authenticated-orcid":false,"given":"Miroslav","family":"Vrankic","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0616-1265","authenticated-orcid":false,"given":"Nikola","family":"Lopac","sequence":"additional","affiliation":[{"name":"Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Croatia"},{"name":"Center for Artificial Intelligence and Cybersecurity, University of Rijeka, 51000 Rijeka, Croatia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5473-6596","authenticated-orcid":false,"given":"Guruprasad Madhale","family":"Jadav","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,11]]},"reference":[{"key":"ref_1","unstructured":"Varsavsky, A., Mareels, I., and Cook, M. (2011). Epileptic Seizures and the EEG: Measurement, Models, Detection and Prediction, Taylor & Francis."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.eswa.2017.05.052","article-title":"Non-linear classifiers applied to EEG analysis for epilepsy seizure detection","volume":"86","author":"Santofimia","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.bspc.2013.08.006","article-title":"Classification of ictal and seizure-free EEG signals using fractional linear prediction","volume":"9","author":"Joshi","year":"2014","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.cmpb.2011.03.009","article-title":"Analysis of normal and epileptic seizure EEG signals using empirical mode decomposition","volume":"104","author":"Pachori","year":"2011","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.bspc.2014.08.014","article-title":"Classification of seizure and seizure-free EEG signals using local binary patterns","volume":"15","author":"Kumar","year":"2015","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.seizure.2017.05.018","article-title":"Epileptic seizure detection based on imbalanced classification and wavelet packet transform","volume":"50","author":"Yuan","year":"2017","journal-title":"Seizure"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1515\/mms-2016-0021","article-title":"Classification of EEG Signals Using Adaptive Time-Frequency Distributions","volume":"23","author":"Khan","year":"2016","journal-title":"Metrol. Meas. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.patrec.2017.03.023","article-title":"A new approach to characterize epileptic seizures using analytic time-frequency flexible wavelet transform and fractal dimension","volume":"94","author":"Sharma","year":"2017","journal-title":"Pattern Recognit. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bhattacharyya, A., Pachori, R.B., Upadhyay, A., and Acharya, U.R. (2017). Tunable-Q Wavelet Transform Based Multiscale Entropy Measure for Automated Classification of Epileptic EEG Signals. Appl. Sci., 7.","DOI":"10.3390\/app7040385"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.bspc.2017.05.008","article-title":"Stockwell transform for epileptic seizure detection from EEG signals","volume":"38","author":"Kalbkhani","year":"2017","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tzallas, A.T., Tsipouras, M.G., and Fotiadis, D.I. (2007, January 22\u201326). The Use of Time-Frequency Distributions for Epileptic Seizure Detection in EEG Recordings. Proceedings of the 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Lyon, France.","DOI":"10.1109\/IEMBS.2007.4352208"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1109\/TITB.2009.2017939","article-title":"Epileptic Seizure Detection in EEGs Using Time\u2013Frequency Analysis","volume":"13","author":"Tzallas","year":"2009","journal-title":"IEEE Trans. Inf. Technol. Biomed."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compbiomed.2016.11.002","article-title":"Algorithm based on the short-term R\u00e9nyi entropy and IF estimation for noisy EEG signals analysis","volume":"80","author":"Lerga","year":"2017","journal-title":"Comput. Biol. Med."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1850030","DOI":"10.1142\/S0129065718500302","article-title":"Time-Varying EEG Correlations Improve Automated Neonatal Seizure Detection","volume":"29","author":"Tapani","year":"2019","journal-title":"Int. J. Neural Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lerga, J., Saulig, N., Stankovi\u0107, L., and Ser\u0161i\u0107, D. (2021). Rule-Based EEG Classifier Utilizing Local Entropy of Time\u2013Frequency Distributions. Mathematics, 9.","DOI":"10.3390\/math9040451"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/s13634-020-00667-6","article-title":"Adaptive filtering and analysis of EEG signals in the time-frequency domain based on the local entropy","volume":"2020","author":"Lerga","year":"2020","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Farooq, M.S., Zulfiqar, A., and Riaz, S. (2023). Epileptic Seizure Detection Using Machine Learning: Taxonomy, Opportunities, and Challenges. Diagnostics, 13.","DOI":"10.3390\/diagnostics13061058"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Khan, N.A., Ali, S., and Choi, K. (2022). Modified Time-Frequency Marginal Features for Detection of Seizures in Newborns. Sensors, 22.","DOI":"10.3390\/s22083036"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Mir, W.A., Anjum, M., and Shahab, S. (2023). Deep-EEG: An Optimized and Robust Framework and Method for EEG-Based Diagnosis of Epileptic Seizure. Diagnostics, 13.","DOI":"10.3390\/diagnostics13040773"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.irbm.2019.02.002","article-title":"Eigenspace Time Frequency Based Features for Accurate Seizure Detection from EEG Data","volume":"40","author":"Deriche","year":"2019","journal-title":"IRBM"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"101943","DOI":"10.1016\/j.jocs.2023.101943","article-title":"Multiple classification of EEG signals and epileptic seizure diagnosis with combined deep learning","volume":"67","year":"2023","journal-title":"J. Comput. Sci."},{"key":"ref_22","unstructured":"Boashash, B. (2016). Time-Frequency Signal Analysis and Processing, A Comprehensive Reference, Elsevier. [2nd ed.]."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2408","DOI":"10.1109\/ACCESS.2021.3139850","article-title":"Detection of Non-Stationary GW Signals in High Noise From Cohen\u2019s Class of Time-Frequency Representations Using Deep Learning","volume":"10","author":"Lopac","year":"2021","journal-title":"IEEE Access"},{"key":"ref_24","unstructured":"Lopac, N. (2022). Detection of Gravitational-Wave Signals from Time-Frequency Distributions Using Deep Learning. [Ph.D. Thesis, University of Rijeka, Faculty of Engineering]."},{"key":"ref_25","unstructured":"Stankovic, L., Dakovic, M., and Thayaparan, T. (2013). Time-Frequency Signal Analysis with Applications, Artech House Publishers."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lopac, N., Lerga, J., and Cuoco, E. (2020). Gravitational-Wave Burst Signals Denoising Based on the Adaptive Modification of the Intersection of Confidence Intervals Rule. Sensors, 20.","DOI":"10.3390\/s20236920"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lopac, N., Lerga, J., Saulig, N., Stankovi\u0107, L., and Dakovi\u0107, M. (2021, January 8\u201311). On Optimal Parameters for ICI-Based Adaptive Filtering Applied to the GWs in High Noise. Proceedings of the 2021 6th International Conference on Smart and Sustainable Technologies (SpliTech), Bol and Split, Croatia.","DOI":"10.23919\/SpliTech52315.2021.9566364"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lopac, N., Jurdana, I., Lerga, J., and Wakabayashi, N. (2021). Particle-Swarm-Optimization-Enhanced Radial-Basis-Function-Kernel-Based Adaptive Filtering Applied to Maritime Data. J. Mar. Sci. Eng., 9.","DOI":"10.3390\/jmse9040439"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1002\/acs.2583","article-title":"Multi-component instantaneous frequency estimation using locally adaptive directional time frequency distributions","volume":"30","author":"Khan","year":"2016","journal-title":"Int. J. Adapt. Control. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.compbiomed.2018.06.018","article-title":"A new feature for the classification of non-stationary signals based on the direction of signal energy in the time\u2013frequency domain","volume":"100","author":"Khan","year":"2018","journal-title":"Comput. Biol. Med."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3154","DOI":"10.1007\/s00034-018-0802-z","article-title":"Locally Optimized Adaptive Directional Time-Frequency Distributions","volume":"37","author":"Mohammadi","year":"2018","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5656","DOI":"10.1007\/s00034-020-01427-5","article-title":"Spike Detection Based on the Adaptive Time-Frequency Analysis","volume":"39","author":"Mohammadi","year":"2020","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1186\/1687-6180-2011-125","article-title":"Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency R\u00e9nyi entropy","volume":"2011","author":"Sucic","year":"2011","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.dsp.2014.07.013","article-title":"Analysis of Local Time-Frequency Entropy Features for Nonstationary Signal Components Time Supports Detection","volume":"34","author":"Sucic","year":"2014","journal-title":"Digit. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Jurdana, V., Volaric, I., and Sucic, V. (2020, January 7\u20139). The Local R\u00e9nyi Entropy Based Shrinkage Algorithm for Sparse TFD Reconstruction. Proceedings of the 2020 International Conference on Broadband Communications for Next Generation Networks and Multimedia Applications (CoBCom), Graz, Austria.","DOI":"10.1109\/CoBCom49975.2020.9174168"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103225","DOI":"10.1016\/j.dsp.2021.103225","article-title":"Sparse time-frequency distribution reconstruction based on the 2D R\u00e9nyi entropy shrinkage algorithm","volume":"118","author":"Jurdana","year":"2021","journal-title":"Digit. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1016\/j.sigpro.2006.10.013","article-title":"IF estimation for multicomponent signals using image processing techniques in the time\u2013frequency domain","volume":"87","author":"Rankine","year":"2007","journal-title":"Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1016\/j.patcog.2014.08.016","article-title":"Principles of time\u2013frequency feature extraction for change detection in non-stationary signals: Applications to newborn EEG abnormality detection","volume":"48","author":"Boashash","year":"2015","journal-title":"Pattern Recognit."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"725189","DOI":"10.1155\/2011\/725189","article-title":"An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR","volume":"2011","author":"Lerga","year":"2011","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1049\/iet-spr.2013.0349","article-title":"Multicomponent noisy signal adaptive instantaneous frequency estimation using components time support information","volume":"8","author":"Sucic","year":"2014","journal-title":"IET Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/S0165-1684(00)00236-X","article-title":"A Measure of Some Time\u2013Frequency Distributions Concentration","volume":"81","year":"2001","journal-title":"Signal Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1109\/18.923723","article-title":"Measuring Time-Frequency Information Content Using the R\u00e9nyi Entropies","volume":"47","author":"Baraniuk","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/LSP.2004.839696","article-title":"Minimum Entropy Time-Frequency Distributions","volume":"12","author":"Aviyente","year":"2005","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Principe, J. (2010). Information Theoretic Learning: Renyi\u2019s Entropy and Kernel Perspectives, Springer.","DOI":"10.1007\/978-1-4419-1570-2"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2227","DOI":"10.1007\/s00034-018-0960-z","article-title":"A Modified Viterbi Algorithm-Based IF Estimation Algorithm for Adaptive Directional Time-Frequency Distributions","volume":"38","author":"Khan","year":"2019","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"108494","DOI":"10.1016\/j.sigpro.2022.108494","article-title":"ADTFD-RANSAC For multi-component IF estimation","volume":"195","author":"Khan","year":"2022","journal-title":"Signal Process."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"102562","DOI":"10.1016\/j.bspc.2021.102562","article-title":"An instantaneous frequency and group delay based feature for classifying EEG signals","volume":"67","author":"Khan","year":"2021","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Khan, N.A., Mohammadi, M., and Choi, K. (2023). A Rule-Based Classifier to Detect Seizures in EEG Signals. Circuits Syst. Signal Process.","DOI":"10.1007\/s00034-022-02281-3"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.compbiomed.2011.10.010","article-title":"Differential operator in seizure detection","volume":"42","author":"Majumdar","year":"2012","journal-title":"Comput. Biol. Med."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.medengphy.2011.08.001","article-title":"A nonparametric feature for neonatal EEG seizure detection based on a representation of pseudo-periodicity","volume":"34","author":"Stevenson","year":"2012","journal-title":"Med. Eng. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Saulig, N., Lerga, J., Mili\u010di\u0107, S., and Tomasovi\u0107, Z. (2022). Block-Adaptive R\u00e9nyi Entropy-Based Denoising for Non-Stationary Signals. Sensors, 22.","DOI":"10.3390\/s22218251"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/10\/4680\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:33:21Z","timestamp":1760124801000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/10\/4680"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,11]]},"references-count":51,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["s23104680"],"URL":"https:\/\/doi.org\/10.3390\/s23104680","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,11]]}}}